Deciphering the $X(3872)$ via its polarization in prompt production at the CERN LHC

Abstract

Based on the hypothesis that the $X(3872)$ exotic hadron is a mixture of ${\chi }_{c1}(2P)$ and other states and that its prompt hadroproduction predominately proceeds via its ${\chi }_{c1}(2P)$ component, we calculate the prompt-$X(3872)$ polarization at the CERN LHC through next-to-leading order in ${\alpha }_s$ within the factorization formalism of nonrelativistic QCD, including both the color-singlet ${}^3{P}_1^{[1]}$ and color-octet ${}^3{S}_1^{[8]}$ $c\bar{c}$ Fock states. We also consider the polarization of the $J/\psi$ produced by the subsequent $X(3872)$ decay. We predict that, under ATLAS, CMS, and LHCb experimental conditions, the $X(3872)$ is largely longitudinally polarized, while the $J/\psi$ is largely transversely polarized. We propose that the LHC experiments perform such polarization measurements to pin down the nature of the $X(3872)$ and other $X$, $Y$, $Z$ exotic states with non-zero spin.

6 pages, 3 figures, matches journal version

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Cited by in corpus (11)

• Observation of multiplicity-dependent prompt ${\chi }_{c1}(3872)$ and $\psi (2S)$ production in $pp$ collisions
• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
• Production of exotic hadrons in $pp$ and nuclear collisions
• $D^{\pm }{D}^{\ast \mp }$ Hadronic Atom as a Key to Revealing the $X(3872)$ Mystery
• Prospects for quarkonium studies at the high-luminosity LHC
• Semi-inclusive lepto-production of hidden-charm exotic hadrons
• Dipole subtraction at next-to-leading order in nonrelativistic-QCD factorization
• How well does nonrelativistic QCD factorization work at next-to-leading order?
• Dipole Subtraction vs. Phase Space Slicing in NLO NRQCD Heavy-Quarkonium Production Calculations
• $S$-wave contributions to the $B_{(s)}\to {\chi }_{c1}(\pi \pi ,K\pi ,KK)$ decays
• Cross sections of inclusive $\psi (2S)$ and $X(3872)$ production from $b$-hadron decays in $pp$ collisions and comparison with ATLAS and CMS data